Forth Week Final Test
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Due DateApril 27, 2:59 AM EDT
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Due Apr 27, 2:59 AM EDT
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For the function f(x,y)={x4+y2x2y, if x2+y2>00, if x2+y2=0 find the value fx′(0,0)+fy′(0,0).
Could the following picture be the plot of levels of a differentiable at (0,0) function?

Correct!
Find the tangent plane to the function f(x,y)=x2+y2 at the point M=(1,2) in the form Ax+By+Cz+D=0. Write the sum A+B+C+D.
By swapping function's change with the differential, find the approximate value of 0.971.05. Write Δx, Δy and calculated value separated by semicolons (all numbers should rounded up to 2 digits).
Assume f(x,y)=x3+y3+xy(x−y). Calculate fxxy′′′(1,1)+fxxx′′′(1,1)+fyyy′′′(1,1).